Saturday, August 29, 2015

New Geometry Unit 0 — Intro to Logic

Since, as @samjshah reminds me, we blog partly as an reflective archive for ourselves, I wanted to capture some of what I did in the new introductory logic unit I created for Geometry this year. I also wanted to capture some of who and what inspired me to do the things that worked out best!

I had no idea how prescient it would be to have an introductory unit that both adds tremendous rigor and depth while simultaneously being somewhat optional. These first two weeks of school have been somewhat chaotic as we discover who has been placed and scheduled correctly, who needs to be placed into a different section due to unavoidable schedule changes, corrections, or updates, how many new sections of certain courses we need, and so on. There were days when I felt like I didn't have the same students in any class two days in a row — even though some days this was more of a feeling than an actuality. So it was wonderful to have an adaptable "throughline" these two weeks — a river into which students might step, flow, or reenter without too much extra craziness. The unit was hard in the good way that students at my school really love — at the Zone of Proximal Development (ZPD), way up on a shelf just high enough above them that they have to stretch to reach it.

DAY 1 — Attacks and Counterattacks — What makes a mathematical definition?
We started with @samjshah and Brendan's Attacks and Counterattacks, which is now the recommended default starting unit for all Geometry students in our district. It was a great icebreaking activity, prompting students to activates their prior knowledge about what constitutes a definition. Plus it involved defining a narwhal, so how could that end badly, right? Table groups passed their definitions around the room, then used table-sized whiteboards to come up with a counterexample that broke the defining group's definitions. This involved both collaboration and presentation skills, as well as a good memory for definitional trivia. Did you know that the horn of the narwhal is ACTUALLY a tooth?

DAY 2 — Statements, Compound Statements, and Truth Tables
I also used this unit to set up classroom norms. Each day, when students come in, the "Welcome" slide is projected onto the board with introductory instructions and the Home Enjoyment (HE) assignment to copy down into your notebook.

We don't have bells at our school, so as an auditory cue, I am taking a page from the amazing @MrVaudrey and embedding a one-minute "welcome to class" music button that tells students this is a short, specific, and finite portion of our show and they know what they need to do. Thank you, Mr. Vaudrey! The theme music for Geometry (my 1st block class at 7:35 a.m.) is the music from Hawaii 5-0 (in honor of my principal and reminding me to ask myself, What Would @wahedahbug Do? with her brilliant mathematical classroom intro routines).

The instructions sometimes tell students to grab a handout from the handouts hanger but they always tell students to get out their HE and compare answers. I have realized that if I need to include homework review during a time of greatest primacy and recency, then I am going to make it count (thank you, @druinok and @pamjwilson!).

Next up was a dramatic table read of a deleted scene from the first Harry Potter movie. It's just terrible what ends up on the cutting room floor but, you know — Hollywood. "Harry Potter and the Logical Statement" was a SMASH hit. Students taught themselves the basics of statements, negations, equivalence, and truth tables and it beat the living crap out of giving them a boring lecture. After they were done, we summarized and organized what we had learned and I set up expectations for Home Enjoyment.

Day 3 —Advanced Equivalence & Rules of Replacement; Intro to Conditional Statements
The beginning of the truth table Olympics. Getting students to use what they know and extend it and — hooray — organize their work logically on the page was a huge win. Plus the kids liked learning something grown-up and hard. We did more practice set up homework review routines and expectations. Students are getting better about coming into class and getting started right away. Overview of the Professionalism score and expectation-setting.

Day 4 —Conditional Statements, Part II
Students discovered the Law of Non-Contradiction (Law of the Excluded Middle: A ⋁ ~A, but not both), and introduction to converse, inverse, and contrapositive using the basic conditional statement, "If I am Batman, then I am a superhero" (I'm looking at you, @mgolding). Whole lot of truth table whiteboarding going on.

Day 5 —Four Basic Laws of Inference
Modus ponens, modus tollens, simplification, disjunctive syllogism, and intro to proof. By this point are really getting into the technical language, to my great surprise. We start whiteboarding proofs and advanced truth tables.

Day 6 — Biconditionals & Definitions
We return full circle to where we started, with definitions, but now we define biconditional (iff) statements and how to prove them. Students start to groove on the idea that you have to prove both if A, then B and also if B, then A to prove a biconditional. There are lightbulb moments about the importance of counterexamples. Routines are starting to gel. Students are still transferring into the class and between/among sections/instructors, but other students help to indoctrinate them into our emerging culture.

Day 7 — Intensive Practice Day — Truth Table Practice aka Whiteboarding Madness
I give each table a sheet of truth tables to build and I use this activity as a Participation Quiz to further solidify our norms. Many groups start passing the marker around to ensure equitable participation. Everybody does splendidly on the Participation Quiz.

Day 8— Assessment
Home Enjoyment Packet #1 is due to be turned in. Students take the Unit 0 Logic test. It is a bear, but my students are "scared but prepared." Some students need more time so they come in at 7:15 a.m., during 3rd, 4th, 5th, or 6th block to finish. Their stillness and concentration is impressive. Algebra 1 students are doing their own crazy stuff all around them, but they persist and persevere. I am over the moon about them. They are proud of themselves for the advanced logic they have learned.

Day 9— Chapter 1 Launch: The Elements of Geometry — the poetry of primitives
We explore undefined terms, learn a little math history, and do some Think-Pair-Share. Next year I want to have another table reading/deleted scene activity for all this stuff instead of a boring lecture. But that is OK. Our routines are solid and we are moving forward.

Onward to constructions on Monday.

Now I have to score 73 logic tests (and 73 HE packets, but only for completion), but it was totally worth it. My Geometry classes are off to a great start, and we have a solid foundation to build from, even if my sections have 36 kids each.

Saturday, August 22, 2015

TMC15 reflection: The Story Of TMC or, How We Didn't Get Lucky

We had our first week with students this week and boy, am I tired.

But all week long, I feel like I've been carried along on the current of good energy I have forged over the years with my TMC (Twitter Math Camp) math teacher tribe.

I was thinking about how other people keep telling me, Oh wow, you're so lucky you've got that.

And I finally realized I've been wanting to say, "No — we didn't get lucky."

A little over four years ago, a bunch of us who had met on Twitter and blogs decided we wanted to get together in real life. In December of 2011, over winter break, there was what is now known as The Great Facebook Friending of 2011. One night during a rampage of funny, crazy, meaningful tweeting among math teacher tweeps, we made the decision to "Facebook-friend" each other.

At the time, that felt like a HUGE risk — letting other people into our real, personal lives.

I was worried that the next morning I would wake up and discover that it had all been an enormous mistake and I would need to go into internet witness protection to get away from these crazies. I was worried that I was going to have such a hangover.

But no. I discovered that these really WERE the people I wanted to be connected with. And other people did too.

So even though Julie Reulbach still wanted us to go on a cruise together, we all decided it would be safer — and saner — to meet on land somewhere. The Mary Institute and Country Day School in St. Louis was gracious enough to offer us a free space to have our math teacher jamboree, and we all traveled from remote parts of North America on our own dimes to get there.

And as I like to remind people who say how lucky we were this year to have TMC at Harvey Mudd College in Southern California — remember that at the first TMC in St. Louis, I was the only person from California who showed up.

We didn't get lucky. We took small, incremental risks with our teaching and with our professional development until we felt safe enough and ready enough to form something larger.

And as the great psychoanalyst and cantadora Clarissa Pinkola Estes has said, when you step forward and truly embrace your whole life with your whole life, other like-minded people will "mysteriously show up, announcing that this is exactly what they have been looking for all along."

In other words, there are rewards for courage.

So my biggest TMC15 reflection is a reminder to myself that we did NOT in any way just "get lucky" with TMC. We stepped forward and showed up in our professional development lives — over and over and over. We stepped over the negative chatter of people all around us saying "there's no such thing as good PD" and we pushed past people who asked negative questions like "Why would you want to use part of your summer vacation time to travel to ______ [fill in the blank with St. Louis/Philadelphia/Jenks, OK/Pasadena] in the summer for professional development?" and we ignored the negativity of anybody in our home districts dumping on "Common Core math" or "all that fancy-schmancy group work nonsense."

We took a deep reflective breath and said a holy "yes" to being deliberate about our teaching practice and taking the risk of investing our whole selves into it. And THAT, as I constantly remind my students, is the essence of "luck."

Wednesday, August 19, 2015

DELETED SCENE: Harry Potter and the Logical Statement — GEO (statements, compound statements, and truth tables)

I'm absolutely slammed for time, but I wanted to share this script I wrote for my Geo students, which was a surprise hit.

I'm taking a page this year from the patented Sam Shah "Here kids, teach yourselves this stuff" pedagogical method, which really deserves a lot more credit than it gets.

I had students act out this "script" which is, of course, from a confidential deleted scene from the first Harry Potter movie. The studio insisted I return all copies after the class. Students delighted in finding the many "problems" with the script and we laughed about all the many reasons why this scene was obviously deleted.

When you release students to launch the task, you want to slam a ruler on the table and yell, "ACTION!"

Students had a lot of fun and got their intro to symbolic logic. Mission accomplished.


The file is available on the Math Teacher Wiki:

Deleted Scene: Harry Potter and the Logical Statement

Friday, July 31, 2015

Have Students Introduce Themselves to Talking Points — Algebra 1 Day 2-ish

With Talking Points, I keep finding that the more I push control down into student groups, the better they self-regulate and dive into the material.

So here is a self-guided intro to Talking Points for Algebra 1 students.

Also, with blind students in the classroom, it becomes even more important for equity that student groups speak and listen equitably to ensure inclusion. So with Talking Points, in addition to handouts, I can give a blind student the Word document on a flash drive, they can plug it into a Braille reader (which allows them to read a line at a time), and everybody is off to the races.

The ever-growing Google Drive folder for new sets of math Talking Points is at

Friday, July 24, 2015

NCTM and The Math Forum Join Forces

Well, here at Twitter Math Camp (#TMC15),  this happened today:

Personally, I am thrilled for my good friends at The Math Forum, who have contributed so much to our extensive worldwide professional learning community. But I also want to witness what a milestone it is for TMC that this is the venue at which the merger was announced.

Five years ago, we were a positive but isolated group of individuals connected by Twitter and by our math teaching blogs. Today, our little conference was the platform for an important piece of news in the math education world.

I have said this before — TMC and the MTBoS (the Math Twitter Blog-o-Sphere) are not a flash in the pan. They represent a paradigm shift. We are a movement. 

They and The Math Forum are living proof that the "market" does not want what focus groups or policy committees think is the safest generic middle course to follow.

They are proof that what is needed — desperately needed — is a community of individuals committed to embodying a better and more sustainable set of principles in our teaching practice and in our professional development lives:
  • Honor the actual work of mathematics teaching that is going on every day — not some sanitized generic ideal that is so removed from reality it cannot be valued.
  • Step forward and be that community you wish you could find. As the great psychoanalyst and cantadora Clarissa Pinkola Estès has written, "if you build that community, people will mysteriously show up, announcing that this is exactly what they have been looking for all along."
  • Witness and celebrate each other's amazing accomplishments in the classroom, even though the power structure and outside forces refuse to accept the good that we do every day. Cheer each other on. This is about "growing up" as a profession and as a community and accepting that true grown-ups do not wait for permission to do what they know what needs to be done. True grown-ups see what needs to be done and say, "Oh, I see. I'll do it."
  • Recognize that this is a movement — and that a movement is what is needed.  We have serious problems, but we have phenomenal capacity to respond to what needs to be done. It is easy to stop a few people, but it is impossible to stop a thousand. Remember the motto of #OtterNation:

  • Don't take "no" for an answer. As @TrianglemanCSD said in his keynote address today, "Find what you love, and do more of it in your classroom."

Tuesday, July 14, 2015

The Primacy-Recency Effect: a conversation with Jennifer Carnes Wilson (episode 1)

Dear Jennifer,

Thanks for engaging with me on David A. Sousa's  The Primacy-Recency Effect article. I too like to reread it and think about it around once a year, so your tweet was most timely for me.

There is a Freudian slip-style of typo in his very first sentence that has always struck me as encapsulating the entire debate he has provoked:
When an individual is processing new information, the amount of information retained depends, among other things on what it is presented during the learning episode. (emphasis mine)
Clearly he means to say "when" rather than "what," but for me, that question of "when" versus "what" lies at the very heart of the debate about student discovery of new ideas. Is it more important when students encounter a new idea or how they encounter it? If I have students tinker and investigate for too long at the beginning of the class period, I risk missing their window of greatest receptivity and retention.

On the other hand, if I start right away by framing the big idea, I harness their optimal moment of receptivity and retention, but am I doing so at the risk of their autonomy?


Tuesday, June 30, 2015

What it means to be a part of a learning community - Tribal Elder Edition

One interesting moment from the Oregon Math Network Conference this past week:

Bill McCallum was leading a large-ish session on building a culture of collaboration through jointly investigating student work.

Fawn (@fawnpnguyen) and I were sitting side by side at a table off to the side, each of us prepping madly for our next sessions. But neither of us could resist the lure of student work. We set our own presentations aside and pulled up the examples of middle school student work on Fawn's computer.

The task for the teachers in the room involved making sense of middle school students' written-out interpretations of different possible takes on how to simplify the expression

                  7 – 2 ( 3 – 8x)

Being experienced teachers of middle school math students, Fawn and I were both immediately captivated.

"Look at how this student identified right away that the value being distributed is a negative 2 — not just a 2," she said. "They noticed that part of it right away."

I nodded.

I noticed the student's language, which indicated a little mid-process magical thinking about the how to distribute multiplication over subtraction: "...because you use order of operations";  "you always do the problem inside the parentheses first"; "...but then "it's a problem that you've got  – 2 on the outside and – 8x on the inside."

"The student is using these phrases as magical incantations," I said. "The rules are still spells to him or her." Fawn agreed.

We both recognized these pieces of productive struggle from our own students's journeys. We dissolved into flow as we started talking about different ways to provoke authentic insight and discovery in our students. This is what is fun about getting together with kindred teacher spirits. It gives us the chance to share a deep kind of noticing that happens automatically during the school year, when we are trying to avoid drowning in the sheer overwhelming volume of student work.

While we'd been lost in analyzing, noticing, and wondering — and unnoticed by us — Bill had stepped closer to eavesdrop on our conversation and to join in the fun. At a certain point, he stepped right into the flow of conversation, offering his own noticings and wonderings about the students' wordings and insights. Several times we all burst out laughing — not at the student's work but at our own pure delight in it. Even after all this time, we can all still be captivated by adolescent mathematical thinking.

Well into his late 80s, Michelangelo was often heard to repeat the motto, "Ancora imparo" — "I am still learning." That is a concise summary of the delight that all teachers feel when we get the chance to sit together as a part of a learning community and think about teaching and learning together. This is the best teaching and learning reminder I know, and I always feel blessed when I have one of these flashes of self-remembering during one of these moments. So I wanted to capture this one.